The steady-state and convergence performances are important indicators to evaluate adaptive algorithms. The step-size affects these two important indicators directly. Many relevant scholars have also proposed some variable step-size adaptive algorithms for improving performance. However, there are still some problems in these existing variable step-size adaptive algorithms, such as the insufficient theoretical analysis, the imbalanced performance and the unachievable parameter. These problems influence the actual performance of some algorithms greatly. Therefore, we intend to further explore an inherent relationship between the key performance and the step-size in this paper. The variation of mean square deviation (MSD) is adopted as the cost function. Based on some theoretical analyses and derivations, a novel variable step-size algorithm with a dynamic limited function (DLF) was proposed. At the same time, the sufficient theoretical analysis is conducted on the weight deviation and the convergence stability. The proposed algorithm is also tested with some typical algorithms in many different environments. Both the theoretical analysis and the experimental result all have verified that the proposed algorithm equips a superior performance.

In this Letter, a robust variable step-size affine-projection subband adaptive filter algorithm (RVSS-APSAF) is proposed, whereby a band-dependent variable step-size is introduced to improve convergence and misalignment performances in impulsive noise environments. Specifically, the weight vector is adaptively updated to achieve robustness against impulsive noises. Finally, the proposed RVSS-APSAF algorithm is tested for system identification in an impulsive noise environment.

Determining an effective way to reduce computation complexity is an essential task for adaptive echo cancellation applications. Recently, a family of partial update (PU) adaptive algorithms has been proposed to effectively reduce computational complexity. However, because a PU algorithm updates only a portion of the weights of the adaptive filters, the rate of convergence is reduced. To address this issue, this paper proposes an enhanced switching-based variable step-size (ES-VSS) approach to the M-max PU least mean square (LMS) algorithm. The step-size is determined by the correlation between the error signals and their noise-free versions. Noise-free error signals are approximated according to the level of convergence achieved during the adaptation process. The approximation of the noise-free error signals switches among four modes, such that the resulting step-size is as close to its optimal value as possible. Simulation results show that when only a half of all taps are updated in a single iteration, the proposed method significantly enhances the convergence rate of the M-max PU LMS algorithm.

Acoustic feedback is a major complaint of hearing aid users. Adaptive filters are a common method for suppressing acoustic feedback in digital hearing aids. In this letter, we propose a new variable step-size algorithm for normalized least mean square and an affine projection algorithm to combine with a variable step-size affine projection algorithm and global speech absence probability in an adaptive filter. The computer simulation used to test the proposed algorithm results in a lower misalignment error than the comparison algorithm at a similar convergence rate. Therefore, the proposed algorithm suggests an effective solution for the feedback suppression system of digital hearing aids.

Recently, proportionate adaptive algorithms have been proposed to speed up convergence in the identification of sparse impulse response. Although they can improve convergence for sparse impulse responses, the steady-state misalignment is limited by the constant step-size parameter. In this article, based on the principle of least perturbation, we first present a derivation of normalized version of proportionate algorithms. Then by taking the disturbance signal into account, we propose a variable step-size proportionate NLMS algorithm to combine the benefits of both variable step-size algorithms and proportionate algorithms. The proposed approach can achieve fast convergence with a large step size when the identification error is large, and then considerably decrease the steady-state misalignment with a small step size after the adaptive filter reaches a certain degree of convergence. Simulation results verify the effectiveness of the proposed approach.

A parallel notch filter (PNF) for eliminating a sinusoidal signal whose frequency and phase are unknown, has been proposed previously. The PNF achieves both fast convergence and high estimation accuracy when the step-size for adaptation is appropriately determined. However, there has been no discussion of how to determine the appropriate step-size. In this paper, we derive the convergence condition on the step-size, and propose an adaptive algorithm with variable step-size so that convergence of the PNF is automatically satisfied. Moreover, we present a new filtering structure of the PNF that increases the convergence speed while keeping the estimation accuracy. We also derive a variable step-size scheme for the new PNF to guarantee the convergence. Simulation results show the effectiveness of the proposed method.

A noise reduction technique that uses the linear prediction to remove noise components in speech signals has been proposed previously. The noise reduction works well for additive white noise signals, because the coefficients of the linear predictor converge such that the prediction error becomes white. In this method, the linear predictor is updated by a gradient-based algorithm with a fixed step-size. However, the optimal value of the step-size changes with the values of the prediction coefficients. In this paper, we propose a noise reduction system using the linear predictor with a variable step-size. The optimal value of the step-size depends also on the variance of the white noise, however the variance is unknown. We therefore introduce a speech/non-speech detector, and estimate the variance in non-speech segments where the observed signal includes only noise components. The simulation results show that the noise reduction capability of the proposed system is better than that of the conventional one with a fixed step-size.

The adaptive cross-spectral (ACS) technique recently introduced by Okuno et al. provides an attractive solution to acoustic echo cancellation (AEC) as it does not require double-talk (DT) detection. In this paper, we first introduce a generalized ACS (GACS) technique where a step-size parameter is used to control the magnitude of the incremental correction applied to the coefficient vector of the adaptive filter. Based on the study of the effects of the step-size on the GACS convergence behaviour, a new variable step-size ACS (VSS-ACS) algorithm is proposed, where the value of the step-size is commanded dynamically by a special finite state machine. Furthermore, the proposed algorithm has a new adaptation scheme to improve the initial convergence rate when the network connection is created. Experimental results show that the new VSS-ACS algorithm outperforms the original ACS in terms of a higher acoustic echo attenuation during DT periods and faster convergence rate.

The minimum mean-squared error (MMSE) linear detector has been proposed to successfully suppress the multiple access interference and mitigate the near-far problem in direct-sequence code-division multiple access communication systems. In the presence of unknown or time-varying channel parameters, the MMSE linear detector can be implemented by the blind Griffiths' algorithm, which uses the desired signal vector instead of a training sequence of symbols for initial adaptation. In this paper, a variable step-size (VSS) Griffiths' algorithm is proposed for accelerating the convergence speed, especially in the presence of strong interference. Numerical results show that the convergence properties of the VSS Griffiths' algorithm are robust against the wide eigenvalue-spread problem of the correlation matrix associated with the received signal vector compared to the Griffiths' algorithm using a fixed step-size.

A new cost function based on multi-band decomposition of the estimation error and application of a different step-size for each band is used in connection with the least-mean-square criterion to improve the fidelity of estimates as compared to those obtained with conventional least-mean-square adaptive algorithms. The basic new idea is to trade off time and frequency resolutions of the adaptive algorithm along the frequency domain by using different step-sizes in the analysis of distinct frequencies in accordance with the frequency-localized statistical behavior of the imput signal. The mathematical background for a stochatic approach to the multi-band decomposition-based scheme is presented and algorithms with fixed and variable step-sizes are derived. Computer experiments compare the performance of multiband and conventional least-mean-square methods when applied to system identification.